More gems from euclidean geometry

he geometry that students encounter in the typical high school course is sometimes merely a collection of synthetic proofs and repetitive exercises, but geometry is more than that. Geometry encompasses unexpected insights, beautiful patterns of interrelated properties, and clever and creative solutions to difficult problems. This article focuses on incorporating some of these more inspiring aspects in the traditional geometry course to infuse students with a greater sense of excitement and wonder in the course, while enrich ing both students' and teachers' perception of and appreciation for this subject. After their struggles to prove the Pythagorean theorem by the traditional ways shown in the high